TESTING OF SCALE PARAMETER OF THE EXPONENTIAL DISTRIBUTION WITH KNOWN COEFFICIENT OF VARIATION: CONDITIONAL APPROACH

ABSTRACT

Tests of hypothesis of the parameter of the reduced exponential distribution E(aθ, θ) has been studied from a conditional viewpoint, based on the conditionality principle of R. A. Fisher. It is shown that conditionally, optimal tests are possible though unconditionally no such test exists. Some desirable properties of the conditional test and large sample approximations to the upper percentile point of the conditional test statistic are also presented. The equivalence of two ancillaries for conditioning with respect to power criterion is shown.

Keywords:

• Conditional inference
• UMP conditional test
• Power function
• Ancillary statistics

ACKNOWLEDGMENTS

This work is part of the Ph.D. thesis submitted by C. D. Ravindran to the Indian Institute of Technology, New Delhi who wishes to acknowledge with thanks the necessary facilities provided by this Institute for carrying out the Ph.D. work and to the Indian Council of Agricultural Research, New Delhi for providing the financial support in the form a doctoral Senior Fellowship. The authors are thankful to referee for providing comments which has helped in improving the presentation of the paper.